]> University of Nebraska-Lincoln

Department of Computer Science and Engineering Lincoln NE 68588-0115 USA xu@unl.edu https://cse.unl.edu/~xu/

University of Colorado at Boulder

Department of Computer Science Boulder CO 80309-0430 USA sangtae.ha@colorado.edu https://netstech.org/sangtaeha/

Bowery Farming

151 W 26TH Street, 12TH Floor New York NY 10001 USA injongrhee@gmail.com

Apple Inc.

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NetApp

Stenbergintie 12 B Kauniainen 02700 FI lars@eggert.org https://eggert.org/

Transport TCPM CUBIC is a standard TCP congestion control algorithm that uses a cubic function instead of a linear congestion window increase function to improve scalability and stability over fast and long-distance networks. CUBIC has been adopted as the default TCP congestion control algorithm by the Linux, Windows, and Apple stacks. This document updates the specification of CUBIC to include algorithmic improvements based on these implementations and recent academic work. Based on the extensive deployment experience with CUBIC, it also moves the specification to the Standards Track, obsoleting RFC 8312. This also requires updating RFC 5681, to allow for CUBIC's occasionally more aggressive sending behavior. About This Document Status information for this document may be found at . Discussion of this document takes place on the TCPM Working Group mailing list (), which is archived at . Subscribe at . Source for this draft and an issue tracker can be found at . Note to the RFC Editor xml2rfc currently renders <em></em> in the XML by surrounding the corresponding text with underscores. This is highly distracting; please manually remove the underscores when doing the final edits to the text version of this document. (There is an issue open against xml2rfc to stop doing this in the future: https://github.com/ietf-tools/xml2rfc/issues/596) Also, please manually change "Figure" to "Equation" for all artwork with anchors beginning with "eq" - xml2rfc doesn't seem to be able to do this.

Introduction CUBIC has been adopted as the default TCP congestion control algorithm in the Linux, Windows, and Apple stacks, and has been used and deployed globally. Extensive, decade-long deployment experience in vastly different Internet scenarios has convincingly demonstrated that CUBIC is safe for deployment on the global Internet and delivers substantial benefits over classical Reno congestion control . It is therefore to be regarded as the currently most widely deployed standard for TCP congestion control. CUBIC can also be used for other transport protocols such as QUIC and SCTP as a default congestion controller. The design of CUBIC was motivated by the well-documented problem classical Reno TCP has with low utilization over fast and long-distance networks . This problem arises from a slow increase of the congestion window following a congestion event in a network with a large bandwidth-delay product (BDP). indicates that this problem is frequently observed even in the range of congestion window sizes over several hundreds of packets. This problem is equally applicable to all Reno-style standards and their variants, including TCP-Reno , TCP-NewReno , SCTP , TFRC , and QUIC congestion control , which use the same linear increase function for window growth. All Reno-style standards and their variants are collectively referred to as "Reno" in this document. CUBIC, originally proposed in , is a modification to the congestion control algorithm of classical Reno to remedy this problem. Specifically, CUBIC uses a cubic function instead of the linear window increase function of Reno to improve scalability and stability under fast and long-distance networks. This document updates the specification of CUBIC to include algorithmic improvements based on the Linux, Windows, and Apple implementations and recent academic work. Based on the extensive deployment experience with CUBIC, it also moves the specification to the Standards Track, obsoleting . This requires an update to , which limits the aggressiveness of Reno TCP implementations. Since CUBIC is occasionally more aggressive than the algorithms, this document updates the first paragraph of , replacing it with a normative reference to guideline (1) in , which allows for CUBIC's behavior as defined in this document. Binary Increase Congestion Control (BIC-TCP) , a predecessor of CUBIC, was selected as the default TCP congestion control algorithm by Linux in the year 2005 and had been used for several years by the Internet community at large. CUBIC uses a similar window increase function as BIC-TCP and is designed to be less aggressive and fairer to Reno in bandwidth usage than BIC-TCP while maintaining the strengths of BIC-TCP such as stability, window scalability, and round-trip time (RTT) fairness. documents the IETF's best current practices for specifying new congestion control algorithms, specifically, ones that differ from the general congestion control principles outlined in . It describes what type of evaluation is expected by the IETF to understand the suitability of a new congestion control algorithm and the process to enable a specification to be approved for widespread deployment in the global Internet. There are areas in which CUBIC differs from the congestion control algorithms previously published in standards-track RFCs; those changes are specified in this document. However, it is not obvious that these changes go beyond the general congestion control principles outlined in , so the process in may not apply. Also, the wide deployment of CUBIC on the Internet was driven by direct adoption in most of the popular operating systems, and did not follow the practices documented in . However, due to the resulting Internet-scale deployment experience over a long period of time, the IETF has determined that CUBIC may be published as a standards-track specification. This decision by the IETF does not alter the general guidance in . The following sections first briefly explain the design principles of CUBIC, provide the exact specification of CUBIC, and finally discuss the safety features of CUBIC following the guidelines specified in .

Conventions The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "NOT RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described in BCP 14 when, and only when, they appear in all capitals, as shown here.

Design Principles of CUBIC CUBIC is designed according to the following design principles:

Principle 1:

For better network utilization and stability, CUBIC uses both the concave and convex profiles of a cubic function to increase the congestion window size, instead of using just a convex function.

Principle 2:

To be Reno-friendly, CUBIC is designed to behave like Reno in networks with short RTTs and small bandwidth where Reno performs well.

Principle 3:

For RTT-fairness, CUBIC is designed to achieve linear bandwidth sharing among flows with different RTTs.

Principle 4:

CUBIC appropriately sets its multiplicative window decrease factor in order to balance between the scalability and convergence speed.

Principle 1 for the CUBIC Increase Function For better network utilization and stability, CUBIC uses a cubic window increase function in terms of the elapsed time from the last congestion event. While most alternative congestion control algorithms to Reno increase the congestion window using convex functions, CUBIC uses both the concave and convex profiles of a cubic function for window growth. After a window reduction in response to a congestion event detected by duplicate ACKs, Explicit Congestion Notification-Echo (ECN-Echo, ECE) ACKs , TCP RACK or QUIC loss detection , CUBIC remembers the congestion window size at which it received the congestion event and performs a multiplicative decrease of the congestion window. When CUBIC enters into congestion avoidance, it starts to increase the congestion window using the concave profile of the cubic function. The cubic function is set to have its plateau at the remembered congestion window size, so that the concave window increase continues until then. After that, the cubic function turns into a convex profile and the convex window increase begins. This style of window adjustment (concave and then convex) improves the algorithm stability while maintaining high network utilization . This is because the window size remains almost constant, forming a plateau around the remembered congestion window size of the last congestion event, where network utilization is deemed highest. Under steady state, most window size samples of CUBIC are close to that remembered congestion window size, thus promoting high network utilization and stability. Note that congestion control algorithms that only use convex functions to increase the congestion window size have their maximum increments around the remembered congestion window size of the last congestion event, and thus introduce many packet bursts around the saturation point of the network, likely causing frequent global loss synchronizations.

Principle 2 for Reno-Friendliness CUBIC promotes per-flow fairness to Reno. Note that Reno performs well over paths with short RTTs and small bandwidths (or small BDPs). There is only a scalability problem in networks with long RTTs and large bandwidths (or large BDPs). A congestion control algorithm designed to be friendly to Reno on a per-flow basis must increase its congestion window less aggressively in small BDP networks than in large BDP networks. The aggressiveness of CUBIC mainly depends on the maximum window size before a window reduction, which is smaller in small-BDP networks than in large-BDP networks. Thus, CUBIC increases its congestion window less aggressively in small-BDP networks than in large-BDP networks. Furthermore, in cases when the cubic function of CUBIC would increase the congestion window less aggressively than Reno, CUBIC simply follows the window size of Reno to ensure that CUBIC achieves at least the same throughput as Reno in small-BDP networks. The region where CUBIC behaves like Reno is called the "Reno-friendly region".

Principle 3 for RTT Fairness Two CUBIC flows with different RTTs have a throughput ratio that is linearly proportional to the inverse of their RTT ratio, where the throughput of a flow is approximately the size of its congestion window divided by its RTT. Specifically, CUBIC maintains a window increase rate independent of RTTs outside the Reno-friendly region, and thus flows with different RTTs have similar congestion window sizes under steady state when they operate outside the Reno-friendly region. This notion of a linear throughput ratio is similar to that of Reno under an asynchronous loss model, where flows with different RTTs have the same packet loss rate but experience loss events at different times. However, under a synchronous loss model, where flows with different RTTs experience loss events at the same time but have different packet loss rates, the throughput ratio of Reno flows with different RTTs is quadratically proportional to the inverse of their RTT ratio . CUBIC always ensures a linear throughput ratio independent of the loss environment. This is an improvement over Reno. While there is no consensus on the optimal throughput ratio for different RTT flows, over wired Internet paths, use of a linear throughput ratio seems more reasonable than equal throughputs (i.e., the same throughput for flows with different RTTs) or a higher-order throughput ratio (e.g., a quadratical throughput ratio of Reno in synchronous loss environments).

Principle 4 for the CUBIC Decrease Factor To balance between scalability and convergence speed, CUBIC sets the multiplicative window decrease factor to 0.7, whereas Reno uses 0.5. While this improves the scalability of CUBIC, a side effect of this decision is slower convergence, especially under low statistical multiplexing. This design choice is following the observation that HighSpeed TCP (HSTCP) and other approaches (e.g., ) made: the current Internet becomes more asynchronous with less frequent loss synchronizations under high statistical multiplexing. In such environments, even strict Multiplicative-Increase Multiplicative-Decrease (MIMD) can converge. CUBIC flows with the same RTT always converge to the same throughput independent of statistical multiplexing, thus achieving intra-algorithm fairness. In environments with sufficient statistical multiplexing, the convergence speed of CUBIC is reasonable.

CUBIC Congestion Control This section discusses how the congestion window is updated during the different stages of the CUBIC congestion controller.

Definitions The unit of all window sizes in this document is segments of the maximum segment size (MSS), and the unit of all times is seconds. Implementations can use bytes to express window sizes, which would require factoring in the maximum segment size wherever necessary and replacing segments_acked with the number of bytes acknowledged in .

Constants of Interest _cubic: CUBIC multiplicative decrease factor as described in . _cubic: CUBIC additive increase factor used in Reno-friendly region as described in . C: constant that determines the aggressiveness of CUBIC in competing with other congestion control algorithms in high BDP networks. Please see for more explanation on how it is set. The unit for C is

Variables of Interest This section defines the variables required to implement CUBIC: RTT: Smoothed round-trip time in seconds, calculated as described in . cwnd: Current congestion window in segments. ssthresh: Current slow start threshold in segments. cwnd_prior: Size of cwnd in segments at the time of setting ssthresh most recently, either upon exiting the first slow start, or just before cwnd was reduced in the last congestion event. W_max: Size of cwnd in segments just before cwnd was reduced in the last congestion event when fast convergence is disabled (same as cwnd_prior on a congestion event). However, if fast convergence is enabled, W_max may be further reduced based on the current saturation point. K: The time period in seconds it takes to increase the congestion window size at the beginning of the current congestion avoidance stage to W_max. t_current: Current time of the system in seconds. t_epoch: The time in seconds at which the current congestion avoidance stage started. cwnd_epoch: The cwnd at the beginning of the current congestion avoidance stage, i.e., at time t_epoch. W_cubic(t): The congestion window in segments at time t in seconds based on the cubic increase function, as described in . target: Target value of congestion window in segments after the next RTT, that is, W_cubic(t + RTT), as described in . W_est: An estimate for the congestion window in segments in the Reno-friendly region, that is, an estimate for the congestion window of Reno. segments_acked: Number of MSS-sized segments acked when a "new ACK" is received, i.e., an ACK that cumulatively acknowledges the delivery of new data. This number will be a decimal value when a new ACK acknowledges an amount of data that is not MSS-sized. Specifically, it can be less than 1 when a new ACK acknowledges a segment smaller than the MSS.

Window Increase Function CUBIC maintains the acknowledgment (ACK) clocking of Reno by increasing the congestion window only at the reception of a new ACK. It does not make any changes to the TCP Fast Recovery and Fast Retransmit algorithms . During congestion avoidance, after a congestion event is detected by mechanisms described in , CUBIC uses a window increase function different from Reno. CUBIC uses the following window increase function:

where t is the elapsed time in seconds from the beginning of the current congestion avoidance stage, that is, and where t_epoch is the time at which the current congestion avoidance stage starts. K is the time period that the above function takes to increase the congestion window size at the beginning of the current congestion avoidance stage to W_max if there are no further congestion events and is calculated using the following equation:

where cwnd_epoch is the congestion window at the beginning of the current congestion avoidance stage. Upon receiving a new ACK during congestion avoidance, CUBIC computes the target congestion window size after the next RTT using as follows, where RTT is the smoothed round-trip time. The lower and upper bounds below ensure that CUBIC's congestion window increase rate is non-decreasing and is less than the increase rate of slow start . 1.5 * cwnd |1.5 * cwnd cubic | | |W (t + RTT) | cubic otherwise \ ]]> The elapsed time t in MUST NOT include periods during which cwnd has not been updated due to application-limited behavior (see ). Depending on the value of the current congestion window size cwnd, CUBIC runs in three different regions:

1. The Reno-friendly region, which ensures that CUBIC achieves at least the same throughput as Reno.
2. The concave region, if CUBIC is not in the Reno-friendly region and cwnd is less than W_max.
3. The convex region, if CUBIC is not in the Reno-friendly region and cwnd is greater than W_max.

To summarize, CUBIC computes both W_cubic(t) and W_est (see ) on receiving a new ACK in congestion avoidance and chooses the larger of the two values. The next sections describe the exact actions taken by CUBIC in each region.

Reno-Friendly Region Reno performs well in certain types of networks, for example, under short RTTs and small bandwidths (or small BDPs). In these networks, CUBIC remains in the Reno-friendly region to achieve at least the same throughput as Reno. The Reno-friendly region is designed according to the analysis in , which studies the performance of an AIMD algorithm with an additive factor of (segments per RTT) and a multiplicative factor of , denoted by AIMD(, ). p is the packet loss rate. Specifically, the average congestion window size of AIMD(, ) can be calculated using .

By the same analysis, to achieve a similar average window size as Reno that uses AIMD(1, 0.5), must be equal to, Thus, CUBIC uses to estimate the window size W_est in the Reno-friendly region with which achieves approximately the same average window size as Reno in many cases. The model used to calculate _cubic is not absolutely precise, but analysis and simulation in , as well as over a decade of experience with CUBIC in the public Internet, show that this approach produces acceptable levels of rate fairness between CUBIC and Reno flows. Also, no significant drawbacks of the model have been reported. However, it would be beneficial to see continued detailed analysis on it. When receiving a new ACK in congestion avoidance (where cwnd could be greater than or less than W_max), CUBIC checks whether W_cubic(t) is less than W_est. If so, CUBIC is in the Reno-friendly region and cwnd SHOULD be set to W_est at each reception of a new ACK. W_est is set equal to cwnd_epoch at the start of the congestion avoidance stage. After that, on every new ACK, W_est is updated using . Note that this equation uses segments_acked and cwnd is measured in segments. An implementation that measures cwnd in bytes should adjust the equation accordingly using number of acknowledged bytes and MSS. Also note that this equation works for connections with enabled or disabled Delayed ACKs , as segments_acked will be different based on the segments actually acknowledged by a new ACK.

Once W_est has grown to reach the cwnd at the time of most recently setting ssthresh, that is, W_est >= cwnd_prior, the sender SHOULD set _cubic to 1 to ensure that it can achieve the same congestion window increment rate as Reno, which uses AIMD(1, 0.5). The next two sections assume that CUBIC is not in the Reno-friendly region and uses the window increase function described in . Although cwnd is incremented in the same way for both concave and convex regions, they are discussed separately to analyze and understand the difference between the two regions.

Concave Region When receiving a new ACK in congestion avoidance, if CUBIC is not in the Reno-friendly region and cwnd is less than W_max, then CUBIC is in the concave region. In this region, cwnd MUST be incremented by for each received new ACK, where target is calculated as described in .

Convex Region When receiving a new ACK in congestion avoidance, if CUBIC is not in the Reno-friendly region and cwnd is larger than or equal to W_max, then CUBIC is in the convex region. The convex region indicates that the network conditions might have changed since the last congestion event, possibly implying more available bandwidth after some flow departures. Since the Internet is highly asynchronous, some amount of perturbation is always possible without causing a major change in available bandwidth. Unless it is overridden by the AIMD window increase, CUBIC is very careful in this region. The convex profile aims to increase the window very slowly at the beginning when cwnd is around W_max and then gradually increases its rate of increase. This region is also called the "maximum probing phase", since CUBIC is searching for a new W_max. In this region, cwnd MUST be incremented by for each received new ACK, where target is calculated as described in .

Multiplicative Decrease When a congestion event is detected by mechanisms described in , CUBIC updates W_max and reduces cwnd and ssthresh immediately as described below. In case of packet loss, the sender MUST reduce cwnd and ssthresh immediately upon entering loss recovery, similar to (and ). Note that other mechanisms, such as Proportional Rate Reduction , can be used to reduce the sending rate during loss recovery more gradually. The parameter _cubic SHOULD be set to 0.7, which is different from the multiplicative decrease factor used in (and ) during fast recovery. In , flight_size is the amount of outstanding (unacknowledged) data in the network, as defined in . Note that a rate-limited application with idle periods or periods when unable to send at the full rate permitted by cwnd could easily encounter notable variations in the volume of data sent from one RTT to another, resulting in flight_size that is significantly less than cwnd when there is a congestion event. The congestion response would therefore decrease cwnd to a much lower value than necessary. To avoid such suboptimal performance, the mechanisms described in can be used. These describe how to manage and use cwnd and ssthresh during a rate-limited Interval, and how to update cwnd and ssthresh after congestion has been detected. The mechanism defined in is safe to use even when cwnd is greater than the receive window, because it validates cwnd based on the amount of data acknowledged by the network in an RTT, which implicitly accounts for the allowed receive window. Some implementations of CUBIC currently use cwnd instead of flight_size when calculating a new ssthresh. Implementations that use cwnd MUST use other measures to prevent cwnd from growing when the volume of bytes in flight is smaller than cwnd. This also effectively avoids cwnd from growing beyond the receive window. Such measures are important to prevent a CUBIC sender from using an arbitrarily high cwnd value when calculating new values for ssthresh and cwnd when congestion is detected. This might not be as robust as the mechanisms described in . A QUIC sender that uses cwnd to calculate new values for cwnd and ssthresh after detecting a congestion event is REQUIRED to apply similar mechanisms .

A side effect of setting _cubic to a value bigger than 0.5 is that packet loss can happen for more than one round-trip in certain cases, but it can work efficiently in other cases, for example, when HyStart++ is used along with CUBIC or when the sending rate is limited by the application. While a more adaptive setting of _cubic could help limit packet loss to a single round, it would require detailed analyses and large-scale evaluations to validate such algorithms. Note that CUBIC MUST continue to reduce cwnd in response to congestion events due to ECN-Echo ACKs until it reaches a value of 1 MSS. If congestion events indicated by ECN-Echo ACKs persist, a sender with a cwnd of 1 MSS MUST reduce its sending rate even further. It can achieve that by using a retransmission timer with exponential backoff, as described in .

Fast Convergence To improve convergence speed, CUBIC uses a heuristic. When a new flow joins the network, existing flows need to give up some of their bandwidth to allow the new flow some room for growth, if the existing flows have been using all the network bandwidth. To speed up this bandwidth release by existing flows, the following "Fast Convergence" mechanism SHOULD be implemented. With Fast Convergence, when a congestion event occurs, W_max is updated as follows, before the window reduction described in . At a congestion event, if the current cwnd is less than W_max, this indicates that the saturation point experienced by this flow is getting reduced because of a change in available bandwidth. This flow can then release more bandwidth by reducing W_max further. This action effectively lengthens the time for this flow to increase its congestion window, because the reduced W_max forces the flow to plateau earlier. This allows more time for the new flow to catch up to its congestion window size. Fast Convergence is designed for network environments with multiple CUBIC flows. In network environments with only a single CUBIC flow and without any other traffic, Fast Convergence SHOULD be disabled.

Timeout In case of a timeout, CUBIC follows Reno to reduce cwnd , but sets ssthresh using _cubic (same as in ) in a way that is different from Reno TCP . During the first congestion avoidance stage after a timeout, CUBIC increases its congestion window size using , where t is the elapsed time since the beginning of the current congestion avoidance, K is set to 0, and W_max is set to the congestion window size at the beginning of the current congestion avoidance stage. In addition, for the Reno-friendly region, W_est SHOULD be set to the congestion window size at the beginning of the current congestion avoidance.

Spurious Congestion Events In cases where CUBIC reduces its congestion window in response to having detected packet loss via duplicate ACKs or timeouts, there is a possibility that the missing ACK would arrive after the congestion window reduction and a corresponding packet retransmission. For example, packet reordering could trigger this behavior. A high degree of packet reordering could cause multiple congestion window reduction events, where spurious losses are incorrectly interpreted as congestion signals, thus degrading CUBIC's performance significantly. For TCP, there are two types of spurious events - spurious timeouts and spurious fast retransmits. In case of QUIC, there are no spurious timeouts as the loss is only detected after receiving an ACK.

Spurious timeout An implementation MAY detect spurious timeouts based on the mechanisms described in Forward RTO-Recovery . Experimental alternatives include Eifel . When a spurious timeout is detected, a TCP implementation MAY follow the response algorithm described in to restore the congestion control state and adapt the retransmission timer to avoid further spurious timeouts.

Spurious loss detected by acknowledgments Upon receiving an ACK, a TCP implementation MAY detect spurious losses either using TCP Timestamps or via D-SACK. Experimental alternatives include Eifel detection algorithm which uses TCP Timestamps and DSACK based detection which uses DSACK information. A QUIC implementation can easily determine a spurious loss if a QUIC packet is acknowledged after it has been marked as lost and the original data has been retransmitted with a new QUIC packet. This section specifies a simple response algorithm when a spurious loss is detected by acknowledgments. Implementations would need to carefully evaluate the impact of using this algorithm in different environments that may experience sudden change in available capacity (e.g., due to variable radio capacity, a routing change, or a mobility event). When a packet loss is detected via acknowledgments, a CUBIC implementation MAY save the current value of the following variables before the congestion window is reduced. Once the previously declared packet loss is confirmed to be spurious, CUBIC MAY restore the original values of the above-mentioned variables as follows if the current cwnd is lower than cwnd_prior. Restoring the original values ensures that CUBIC's performance is similar to what it would be without spurious losses. if cwnd < cwnd | prior K = undo_K | | t = undo_t | epoch epoch | | W = undo_W | est est / ]]> In rare cases, when the detection happens long after a spurious loss event and the current cwnd is already higher than cwnd_prior, CUBIC SHOULD continue to use the current and the most recent values of these variables.

Slow Start CUBIC MUST employ a slow-start algorithm, when cwnd is no more than ssthresh. In general, CUBIC SHOULD use the HyStart++ slow start algorithm , or MAY use the Reno TCP slow start algorithm in the rare cases when HyStart++ is not suitable. Experimental alternatives include hybrid slow start , a predecessor to HyStart++ that some CUBIC implementations have used as the default for the last decade, and limited slow start . Whichever start-up algorithm is used, work might be needed to ensure that the end of slow start and the first multiplicative decrease of congestion avoidance work well together. When CUBIC uses HyStart++ , it may exit the first slow start without incurring any packet loss and thus W_max is undefined. In this special case, CUBIC sets cwnd_prior = cwnd and switches to congestion avoidance. It then increases its congestion window size using , where t is the elapsed time since the beginning of the current congestion avoidance, K is set to 0, and W_max is set to the congestion window size at the beginning of the current congestion avoidance stage.

Discussion This section further discusses the safety features of CUBIC following the guidelines specified in . With a deterministic loss model where the number of packets between two successive packet losses is always 1/p, CUBIC always operates with the concave window profile, which greatly simplifies the performance analysis of CUBIC. The average window size of CUBIC (see ) can be obtained by the following function:

With _cubic set to 0.7, the above formula reduces to:

The following subsection will determine the value of C using .

Fairness to Reno In environments where Reno is able to make reasonable use of the available bandwidth, CUBIC does not significantly change this state. Reno performs well in the following two types of networks:

1. networks with a small bandwidth-delay product (BDP)
2. networks with a short RTTs, but not necessarily a small BDP

CUBIC is designed to behave very similarly to Reno in the above two types of networks. The following two tables show the average window sizes of Reno TCP, HSTCP, and CUBIC TCP. The average window sizes of Reno TCP and HSTCP are from . The average window size of CUBIC is calculated using and the CUBIC Reno-friendly region for three different values of C. Reno TCP, HSTCP, and CUBIC with RTT = 0.1 seconds

Loss Rate P	Reno	HSTCP	CUBIC (C=0.04)	CUBIC (C=0.4)	CUBIC (C=4)
1.0e-02	12	12	12	12	12
1.0e-03	38	38	38	38	59
1.0e-04	120	263	120	187	333
1.0e-05	379	1795	593	1054	1874
1.0e-06	1200	12280	3332	5926	10538
1.0e-07	3795	83981	18740	33325	59261
1.0e-08	12000	574356	105383	187400	333250

describes the response function of Reno TCP, HSTCP, and CUBIC in networks with RTT = 0.1 seconds. The average window size is in MSS-sized segments. Reno TCP, HSTCP, and CUBIC with RTT = 0.01 seconds

Loss Rate P	Reno	HSTCP	CUBIC (C=0.04)	CUBIC (C=0.4)	CUBIC (C=4)
1.0e-02	12	12	12	12	12
1.0e-03	38	38	38	38	38
1.0e-04	120	263	120	120	120
1.0e-05	379	1795	379	379	379
1.0e-06	1200	12280	1200	1200	1874
1.0e-07	3795	83981	3795	5926	10538
1.0e-08	12000	574356	18740	33325	59261

describes the response function of Reno TCP, HSTCP, and CUBIC in networks with RTT = 0.01 seconds. The average window size is in MSS-sized segments. Both tables show that CUBIC with any of these three C values is more friendly to Reno TCP than HSTCP, especially in networks with a short RTT where Reno TCP performs reasonably well. For example, in a network with RTT = 0.01 seconds and p=10^-6, Reno TCP has an average window of 1200 packets. If the packet size is 1500 bytes, then Reno TCP can achieve an average rate of 1.44 Gbps. In this case, CUBIC with C=0.04 or C=0.4 achieves exactly the same rate as Reno TCP, whereas HSTCP is about ten times more aggressive than Reno TCP. C determines the aggressiveness of CUBIC in competing with other congestion control algorithms for bandwidth. CUBIC is more friendly to Reno TCP, if the value of C is lower. However, it is NOT RECOMMENDED to set C to a very low value like 0.04, since CUBIC with a low C cannot efficiently use the bandwidth in fast and long-distance networks. Based on these observations and extensive deployment experience, C=0.4 seems to give a good balance between Reno-friendliness and aggressiveness of window increase. Therefore, C SHOULD be set to 0.4. With C set to 0.4, is reduced to:

is then used in the next subsection to show the scalability of CUBIC.

Using Spare Capacity CUBIC uses a more aggressive window increase function than Reno for fast and long-distance networks. The following table shows that to achieve the 10 Gbps rate, Reno TCP requires a packet loss rate of 2.0e-10, while CUBIC TCP requires a packet loss rate of 2.9e-8. Required packet loss rate for Reno TCP, HSTCP, and CUBIC to achieve a certain throughput

Throughput (Mbps)	Average W	Reno P	HSTCP P	CUBIC P
1	8.3	2.0e-2	2.0e-2	2.0e-2
10	83.3	2.0e-4	3.9e-4	2.9e-4
100	833.3	2.0e-6	2.5e-5	1.4e-5
1000	8333.3	2.0e-8	1.5e-6	6.3e-7
10000	83333.3	2.0e-10	1.0e-7	2.9e-8

describes the required packet loss rate for Reno TCP, HSTCP, and CUBIC to achieve a certain throughput, with 1500-byte packets and an RTT of 0.1 seconds. The test results in indicate that, in typical cases with a degree of background traffic, CUBIC uses the spare bandwidth left unused by existing Reno TCP flows in the same bottleneck link without taking away much bandwidth from the existing flows.

Difficult Environments CUBIC is designed to remedy the poor performance of Reno in fast and long-distance networks.

Investigating a Range of Environments CUBIC has been extensively studied using simulations, testbed emulations, Internet experiments, and Internet measurements, covering a wide range of network environments . They have convincingly demonstrated that CUBIC delivers substantial benefits over classical Reno congestion control . Same as Reno, CUBIC is a loss-based congestion control algorithm. Because CUBIC is designed to be more aggressive (due to a faster window increase function and bigger multiplicative decrease factor) than Reno in fast and long-distance networks, it can fill large drop-tail buffers more quickly than Reno and increases the risk of a standing queue . In this case, proper queue sizing and management could be used to mitigate the risk to some extent and reduce the packet queuing delay. Also, in large-BDP networks after a congestion event, CUBIC, due its cubic window increase function, recovers quickly to the highest link utilization point. This means that link utilization is less sensitive to an active queue management (AQM) target that is lower than the amplitude of the whole sawtooth. Similar to Reno, the performance of CUBIC as a loss-based congestion control algorithm suffers in networks where a packet loss is not a good indication of bandwidth utilization, such as wireless or mobile networks .

Protection against Congestion Collapse With regard to the potential of causing congestion collapse, CUBIC behaves like Reno, since CUBIC modifies only the window adjustment algorithm of Reno. Thus, it does not modify the ACK clocking and timeout behaviors of Reno. CUBIC also satisfies the "full backoff" requirement as described in . After reducing the sending rate to one packet per RTT in response to congestion events due to ECN-Echo ACKs, CUBIC then exponentially increases the transmission timer for each packet retransmission while congestion persists.

Fairness within the Alternative Congestion Control Algorithm CUBIC ensures convergence of competing CUBIC flows with the same RTT in the same bottleneck links to an equal throughput. When competing flows have different RTT values, their throughput ratio is linearly proportional to the inverse of their RTT ratios. This is true independently of the level of statistical multiplexing on the link. The convergence time depends on the network environments (e.g., bandwidth, RTT) and the level of statistical multiplexing, as mentioned in .

Performance with Misbehaving Nodes and Outside Attackers CUBIC does not introduce new entities or signals, so its vulnerability to misbehaving nodes or attackers is unchanged from Reno.

Behavior for Application-Limited Flows A flow is application-limited if it is currently sending less than what is allowed by the congestion window. This can happen if the flow is limited by either the sender application or the receiver application (via the receiver advertised window) and thus sends less data than what is allowed by the sender's congestion window. CUBIC does not increase its congestion window if a flow is application-limited. requires that t in does not include application-limited periods, such as idle periods, otherwise W_cubic(t) might be very high after restarting from these periods.

Responses to Sudden or Transient Events If there is a sudden increase in capacity, e.g., due to variable radio capacity, a routing change, or a mobility event, CUBIC is designed to utilize the newly available capacity faster than Reno. On the other hand, if there is a sudden decrease in capacity, CUBIC reduces more slowly than Reno. This remains true regardless of whether CUBIC is in Reno-friendly mode and regardless of whether fast convergence is enabled.

Incremental Deployment CUBIC requires only changes to the congestion control at the sender, and it does not require any changes at receivers. That is, a CUBIC sender works correctly with Reno receivers. In addition, CUBIC does not require any changes to routers and does not require any assistance from routers.

Security Considerations CUBIC makes no changes to the underlying security of TCP. More information about TCP security concerns can be found in .

IANA Considerations This document does not require any IANA actions.

References Normative References This document defines TCP's four intertwined congestion control algorithms: slow start, congestion avoidance, fast retransmit, and fast recovery. In addition, the document specifies how TCP should begin transmission after a relatively long idle period, as well as discussing various acknowledgment generation methods. This document obsoletes RFC 2581. [STANDARDS-TRACK] RFC 5681 documents the following four intertwined TCP congestion control algorithms: slow start, congestion avoidance, fast retransmit, and fast recovery. RFC 5681 explicitly allows certain modifications of these algorithms, including modifications that use the TCP Selective Acknowledgment (SACK) option (RFC 2883), and modifications that respond to "partial acknowledgments" (ACKs that cover new data, but not all the data outstanding when loss was detected) in the absence of SACK. This document describes a specific algorithm for responding to partial acknowledgments, referred to as "NewReno". This response to partial acknowledgments was first proposed by Janey Hoe. This document obsoletes RFC 3782. [STANDARDS-TRACK] This document presents a conservative loss recovery algorithm for TCP that is based on the use of the selective acknowledgment (SACK) TCP option. The algorithm presented in this document conforms to the spirit of the current congestion control specification (RFC 5681), but allows TCP senders to recover more effectively when multiple segments are lost from a single flight of data. This document obsoletes RFC 3517 and describes changes from it. [STANDARDS-TRACK] This document specifies TCP Friendly Rate Control (TFRC). TFRC is a congestion control mechanism for unicast flows operating in a best-effort Internet environment. It is reasonably fair when competing for bandwidth with TCP flows, but has a much lower variation of throughput over time compared with TCP, making it more suitable for applications such as streaming media where a relatively smooth sending rate is of importance. This document obsoletes RFC 3448 and updates RFC 4342. [STANDARDS-TRACK] This document describes loss detection and congestion control mechanisms for QUIC. The IETF's standard congestion control schemes have been widely shown to be inadequate for various environments (e.g., high-speed networks). Recent research has yielded many alternate congestion control schemes that significantly differ from the IETF's congestion control principles. Using these new congestion control schemes in the global Internet has possible ramifications to both the traffic using the new congestion control and to traffic using the currently standardized congestion control. Therefore, the IETF must proceed with caution when dealing with alternate congestion control proposals. The goal of this document is to provide guidance for considering alternate congestion control algorithms within the IETF. This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements. The goal of this document is to explain the need for congestion control in the Internet, and to discuss what constitutes correct congestion control. This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements. In many standards track documents several words are used to signify the requirements in the specification. These words are often capitalized. This document defines these words as they should be interpreted in IETF documents. This document specifies an Internet Best Current Practices for the Internet Community, and requests discussion and suggestions for improvements. RFC 2119 specifies common key words that may be used in protocol specifications. This document aims to reduce the ambiguity by clarifying that only UPPERCASE usage of the key words have the defined special meanings. This memo specifies the incorporation of ECN (Explicit Congestion Notification) to TCP and IP, including ECN's use of two bits in the IP header. [STANDARDS-TRACK] This document presents the RACK-TLP loss detection algorithm for TCP. RACK-TLP uses per-segment transmit timestamps and selective acknowledgments (SACKs) and has two parts. Recent Acknowledgment (RACK) starts fast recovery quickly using time-based inferences derived from acknowledgment (ACK) feedback, and Tail Loss Probe (TLP) leverages RACK and sends a probe packet to trigger ACK feedback to avoid retransmission timeout (RTO) events. Compared to the widely used duplicate acknowledgment (DupAck) threshold approach, RACK-TLP detects losses more efficiently when there are application-limited flights of data, lost retransmissions, or data packet reordering events. It is intended to be an alternative to the DupAck threshold approach. This document defines the standard algorithm that Transmission Control Protocol (TCP) senders are required to use to compute and manage their retransmission timer. It expands on the discussion in Section 4.2.3.1 of RFC 1122 and upgrades the requirement of supporting the algorithm from a SHOULD to a MUST. This document obsoletes RFC 2988. [STANDARDS-TRACK] The purpose of this document is to move the F-RTO (Forward RTO-Recovery) functionality for TCP in RFC 4138 from Experimental to Standards Track status. The F-RTO support for Stream Control Transmission Protocol (SCTP) in RFC 4138 remains with Experimental status. See Appendix B for the differences between this document and RFC 4138. Spurious retransmission timeouts cause suboptimal TCP performance because they often result in unnecessary retransmission of the last window of data. This document describes the F-RTO detection algorithm for detecting spurious TCP retransmission timeouts. F-RTO is a TCP sender-only algorithm that does not require any TCP options to operate. After retransmitting the first unacknowledged segment triggered by a timeout, the F-RTO algorithm of the TCP sender monitors the incoming acknowledgments to determine whether the timeout was spurious. It then decides whether to send new segments or retransmit unacknowledged segments. The algorithm effectively helps to avoid additional unnecessary retransmissions and thereby improves TCP performance in the case of a spurious timeout. [STANDARDS-TRACK] Based on an appropriate detection algorithm, the Eifel response algorithm provides a way for a TCP sender to respond to a detected spurious timeout. It adapts the retransmission timer to avoid further spurious timeouts and (depending on the detection algorithm) can avoid the often unnecessary go-back-N retransmits that would otherwise be sent. In addition, the Eifel response algorithm restores the congestion control state in such a way that packet bursts are avoided. [STANDARDS-TRACK] This note defines an extension of the Selective Acknowledgement (SACK) Option for TCP. [STANDARDS-TRACK] Confluent Microsoft Microsoft This document describes HyStart++, a simple modification to the slow start phase of congestion control algorithms. Traditional slow start can overshoot the ideal send rate in many cases, causing high packet loss and poor performance. HyStart++ uses a delay increase heuristic to find an exit point before possible overshoot. It also adds a mitigation to prevent jitter from causing premature slow start exit. This memo presents recommendations to the Internet community concerning measures to improve and preserve Internet performance. It presents a strong recommendation for testing, standardization, and widespread deployment of active queue management (AQM) in network devices to improve the performance of today's Internet. It also urges a concerted effort of research, measurement, and ultimate deployment of AQM mechanisms to protect the Internet from flows that are not sufficiently responsive to congestion notification. Based on 15 years of experience and new research, this document replaces the recommendations of RFC 2309. Informative References North Carolina State University, Raleigh, NC North Carolina State University, Raleigh, NC University of Nebraska, Lincoln, Nebraska CERN-IT Division, Geneva, Switzerland This document defines the core of the QUIC transport protocol. QUIC provides applications with flow-controlled streams for structured communication, low-latency connection establishment, and network path migration. QUIC includes security measures that ensure confidentiality, integrity, and availability in a range of deployment circumstances. Accompanying documents describe the integration of TLS for key negotiation, loss detection, and an exemplary congestion control algorithm. This document describes the Stream Control Transmission Protocol (SCTP) and obsoletes RFC 4960. It incorporates the specification of the chunk flags registry from RFC 6096 and the specification of the I bit of DATA chunks from RFC 7053. Therefore, RFCs 6096 and 7053 are also obsoleted by this document. In addition, RFCs 4460 and 8540, which describe errata for SCTP, are obsoleted by this document. SCTP was originally designed to transport Public Switched Telephone Network (PSTN) signaling messages over IP networks. It is also suited to be used for other applications, for example, WebRTC. SCTP is a reliable transport protocol operating on top of a connectionless packet network, such as IP. It offers the following services to its users: The design of SCTP includes appropriate congestion avoidance behavior and resistance to flooding and masquerade attacks. The proposals in this document are experimental. While they may be deployed in the current Internet, they do not represent a consensus that this is the best method for high-speed congestion control. In particular, we note that alternative experimental proposals are likely to be forthcoming, and it is not well understood how the proposals in this document will interact with such alternative proposals. This document proposes HighSpeed TCP, a modification to TCP's congestion control mechanism for use with TCP connections with large congestion windows. The congestion control mechanisms of the current Standard TCP constrains the congestion windows that can be achieved by TCP in realistic environments. For example, for a Standard TCP connection with 1500-byte packets and a 100 ms round-trip time, achieving a steady-state throughput of 10 Gbps would require an average congestion window of 83,333 segments, and a packet drop rate of at most one congestion event every 5,000,000,000 packets (or equivalently, at most one congestion event every 1 2/3 hours). This is widely acknowledged as an unrealistic constraint. To address his limitation of TCP, this document proposes HighSpeed TCP, and solicits experimentation and feedback from the wider community. CUBIC is an extension to the current TCP standards. It differs from the current TCP standards only in the congestion control algorithm on the sender side. In particular, it uses a cubic function instead of a linear window increase function of the current TCP standards to improve scalability and stability under fast and long-distance networks. CUBIC and its predecessor algorithm have been adopted as defaults by Linux and have been used for many years. This document provides a specification of CUBIC to enable third-party implementations and to solicit community feedback through experimentation on the performance of CUBIC. This document describes an experimental Proportional Rate Reduction (PRR) algorithm as an alternative to the widely deployed Fast Recovery and Rate-Halving algorithms. These algorithms determine the amount of data sent by TCP during loss recovery. PRR minimizes excess window adjustments, and the actual window size at the end of recovery will be as close as possible to the ssthresh, as determined by the congestion control algorithm. This document provides a mechanism to address issues that arise when TCP is used for traffic that exhibits periods where the sending rate is limited by the application rather than the congestion window. It provides an experimental update to TCP that allows a TCP sender to restart quickly following a rate-limited interval. This method is expected to benefit applications that send rate-limited traffic using TCP while also providing an appropriate response if congestion is experienced. This document also evaluates the Experimental specification of TCP Congestion Window Validation (CWV) defined in RFC 2861 and concludes that RFC 2861 sought to address important issues but failed to deliver a widely used solution. This document therefore reclassifies the status of RFC 2861 from Experimental to Historic. This document obsoletes RFC 2861. The Eifel detection algorithm allows a TCP sender to detect a posteriori whether it has entered loss recovery unnecessarily. It requires that the TCP Timestamps option defined in RFC 1323 be enabled for a connection. The Eifel detection algorithm makes use of the fact that the TCP Timestamps option eliminates the retransmission ambiguity in TCP. Based on the timestamp of the first acceptable ACK that arrives during loss recovery, it decides whether loss recovery was entered unnecessarily. The Eifel detection algorithm provides a basis for future TCP enhancements. This includes response algorithms to back out of loss recovery by restoring a TCP sender's congestion control state. This memo defines an Experimental Protocol for the Internet community. TCP and Stream Control Transmission Protocol (SCTP) provide notification of duplicate segment receipt through Duplicate Selective Acknowledgement (DSACKs) and Duplicate Transmission Sequence Number (TSN) notification, respectively. This document presents conservative methods of using this information to identify unnecessary retransmissions for various applications. This memo defines an Experimental Protocol for the Internet community. This document describes an optional modification for TCP's slow-start for use with TCP connections with large congestion windows. For TCP connections that are able to use congestion windows of thousands (or tens of thousands) of MSS-sized segments (for MSS the sender's MAXIMUM SEGMENT SIZE), the current slow-start procedure can result in increasing the congestion window by thousands of segments in a single round-trip time. Such an increase can easily result in thousands of packets being dropped in one round-trip time. This is often counter-productive for the TCP flow itself, and is also hard on the rest of the traffic sharing the congested link. This note describes Limited Slow-Start as an optional mechanism for limiting the number of segments by which the congestion window is increased for one window of data during slow-start, in order to improve performance for TCP connections with large congestion windows. This memo defines an Experimental Protocol for the Internet community. Active Queue Management (AQM) mechanisms allow for burst tolerance while enforcing short queues to minimise the time that packets spend enqueued at a bottleneck. This can cause noticeable performance degradation for TCP connections traversing such a bottleneck, especially if there are only a few flows or their bandwidth-delay product (BDP) is large. The reception of a Congestion Experienced (CE) Explicit Congestion Notification (ECN) mark indicates that an AQM mechanism is used at the bottleneck, and the bottleneck network queue is therefore likely to be short. Feedback of this signal allows the TCP sender-side ECN reaction in congestion avoidance to reduce the Congestion Window (cwnd) by a smaller amount than the congestion control algorithm's reaction to inferred packet loss. Therefore, this specification defines an experimental change to the TCP reaction specified in RFC 3168, as permitted by RFC 8311.

Acknowledgments Richard Scheffenegger and Alexander Zimmermann originally co-authored . These individuals suggested improvements to this document:

Evolution of CUBIC

Since draft-ietf-tcpm-rfc8312bis-13

• Add contents of to .
• Multiple comments from Martin, define synchronized/asynchronized loss model, clean up 3465 reference, clarficiation for when Cubic is not in Reno-friendly region, referring to proof of avg Cubic window, better text for misbehaving nodes and fix typo in cwnd_epoch. (#158)

Since draft-ietf-tcpm-rfc8312bis-12

• Fix plaintext version of .

Since draft-ietf-tcpm-rfc8312bis-11

• Fix various nits. (#157)

Since draft-ietf-tcpm-rfc8312bis-10

• Improve text related to . (#149)
• Made variable naming a bit more consistent. (#156)

Since draft-ietf-tcpm-rfc8312bis-09

• Improve text for Reno friendliness, multiplicative decrease and reference to HLRX07. (#152)

Since draft-ietf-tcpm-rfc8312bis-08

• Fix the text specifying when alpha_cubic SHOULD be set to 1 to indicate this should happen when cwnd >= cwnd_prior rather than cwnd >= W_max, since these are different in the fast convergence case (#146)
• Restrict use of cwnd directly on a congestion event (#148)

Since draft-ietf-tcpm-rfc8312bis-07

• Document the WG discussion and decision around and (#145)

Since draft-ietf-tcpm-rfc8312bis-06

• RFC7661 is safe even when cwnd grows beyond rwnd (#143)

Since draft-ietf-tcpm-rfc8312bis-05

• Clarify meaning of "application-limited" in Section 5.8 (#137)
• Create new subsections for spurious timeouts and spurious loss via ACK (#90)
• Brief discussion of convergence in Section 5.6 (#96)
• Add more test results to Section 5 and update some references (#91)
• Change wording around setting ssthresh (#131)

Since draft-ietf-tcpm-rfc8312bis-04

• Fix incorrect math (#106)
• Update RFC5681 (#99)
• Rephrase text around algorithmic alternatives, add HyStart++ (#85, #86, #90)
• Clarify what we mean by "new ACK" and use it in the text in more places. (#101)
• Rewrite the Responses to Sudden or Transient Events section (#98)
• Remove confusing text about cwnd_epoch in Section 4.2 (#100)
• Change terminology from "AIMD" to "Reno" (#108)
• Moved MUST NOT from app-limited section to main cubic AI section (#97)
• Clarify cwnd decrease during multiplicative decrease (#102)
• Clarify text around queuing and slow adaptation of CUBIC in wireless environments (#94)
• Set lower bound of cwnd to 1 MSS and use retransmit timer thereafter (#83)
• Use FlightSize instead of cwnd to update ssthresh (#114)

Since draft-ietf-tcpm-rfc8312bis-03

• Remove reference from abstract (#82)

Since draft-ietf-tcpm-rfc8312bis-02

• Description of packet loss rate p (#65)
• Clarification of TCP Friendly Equation for ABC and Delayed ACK (#66)
• add applicability to QUIC and SCTP (#61)
• clarity on setting alpha_aimd to 1 (#68)
• introduce alpha_cubic (#64)
• clarify cwnd growth in convex region (#69)
• add guidance for using bytes and mention that segments count is decimal (#67)
• add loss events detected by RACK and QUIC loss detection (#62)

Since draft-ietf-tcpm-rfc8312bis-01

• address Michael Scharf's editorial suggestions. (#59)
• add "Note to the RFC Editor" about removing underscores

Since draft-ietf-tcpm-rfc8312bis-00

• use updated xml2rfc with better text rendering of subscripts

Since draft-eggert-tcpm-rfc8312bis-03

• fix spelling nits
• rename to draft-ietf
• define W_max more clearly

Since draft-eggert-tcpm-rfc8312bis-02

• add definition for segments_acked and alpha_aimd. (#47)
• fix a mistake in W_max calculation in the fast convergence section. (#51)
• clarity on setting ssthresh and cwnd_epoch during multiplicative decrease. (#53)

Since draft-eggert-tcpm-rfc8312bis-01

• rename TCP-Friendly to AIMD-Friendly and rename Standard TCP to AIMD TCP to avoid confusion as CUBIC has been widely used on the Internet. (#38)
• change introductory text to reflect the significant broader deployment of CUBIC on the Internet. (#39)
• rephrase introduction to avoid referring to variables that have not been defined yet.

Since draft-eggert-tcpm-rfc8312bis-00

• acknowledge former co-authors (#15)
• prevent cwnd from becoming less than two (#7)
• add list of variables and constants (#5, #6)
• update K's definition and add bounds for CUBIC target cwnd (#1, #14)
• update W_est to use AIMD approach (#20)

• set alpha_aimd to 1 once W_est reaches W_max (#2)
• add Vidhi as co-author (#17)
• note for Fast Recovery during cwnd decrease due to congestion event (#11)
• add section for spurious congestion events (#23)
• initialize W_est after timeout and remove variable W_{last_max} (#28)

Since RFC8312

• converted to Markdown and xml2rfc v3
• updated references (as part of the conversion)
• updated author information
• various formatting changes
• move to Standards Track

Since the Original Paper CUBIC has gone through a few changes since the initial release of its algorithm and implementation. This section highlights the differences between the original paper and .

• The original paper includes the pseudocode of CUBIC implementation using Linux's pluggable congestion control framework, which excludes system-specific optimizations. The simplified pseudocode might be a good source to start with and understand CUBIC.
• also includes experimental results showing its performance and fairness.

• The definition of beta_cubic constant was changed in . For example, beta_cubic in the original paper was the window decrease constant while changed it to CUBIC multiplication decrease factor. With this change, the current congestion window size after a congestion event in was beta_cubic * W_max while it was (1-beta_cubic) * W_max in the original paper.
• Its pseudocode used W_{last_max} while used W_max.
• Its AIMD-friendly window was W_tcp while used W_est.

Proof of the Average CUBIC Window Size This appendix contains a proof for the average CUBIC window size AVG_W_cubic in . We find AVG_W_cubic under a deterministic loss model, where the number of packets between two successive packet losses is 1/p. With this model, CUBIC always operates with the concave window profile and the time period between two successive packet losses is K. The average window size AVG_W_cubic is defined as follows, where the numerator 1/p is the total number of packets between two successive packet losses, and the denominator K/RTT is the total number of RTTs between two successive packet losses.

Below, we find K as a function of CUBIC parameters _cubic and C, and network parameters p and RTT. According to the definition of K in , we have

The total number of packets between two successive packet losses can also be obtained as follows using the window increase function in . Specifically, the window size in the first RTT (i.e., n=1 or equivalently t=0) is C(-K)³+W_max and the window size in the last RTT (i.e., n=K/RTT or equivalently t=K-RTT) is C(-RTT)³+W_max.

After solving and for K and W_max, we have

The average CUBIC window size AVG_W_cubic can be obtained by substituting K with in